The last-32, first leg pitted the world's richest club by income, with annual revenues of more than 600 million euros (473.28 million pounds), against a club with a budget of around 1 million euros a season, who were promoted to Spain's regional Segunda B for the first time at the end of last term.
Despite the glaring mismatch, Barcelona-based Cornella, whose players include a dentist and a school teacher, were not overawed by the occasion and after Varane nodded Real in front from a James Rodriguez corner in the 10th minute, burly striker Oscar Munoz levelled in the 20th with a fierce strike.
France centre back Varane made it 2-1 from Isco's corner in the 36th minute and Javier Hernandez struck eight minutes into the second half before substitute Marcelo rifled home the rebound from an Isco effort 15 minutes from time.
"It was important to get a good win in this first leg," Hernandez said in an interview with Spanish television broadcaster Canal Plus.
"With all our opponents the coach asks us to be professional and we treated this game in exactly the same way as we would a ‘Clasico’ (against Barcelona)," added the Mexican, who is on loan at Real from Manchester United.
Cornella play their home games at the club’s modest 1,500-capacity stadium but Wednesday's match was relocated to Espanyol’s 41,000–seater arena next door.
The stadium was at least half full, with plenty of Barcelona-based Real fans turning out to see their team despite the absence of regulars like Cristiano Ronaldo, the injured Gareth Bale and Iker Casillas.
Spanish media reported the Cornella players had been promised a bonus of around 1,400 euros if they achieve the feat of eliminating Real, less than Ronaldo earns in a single hour.
"We had to make the most of the fact that we were playing in front of so many people for the first time," Munoz told Canal Plus.
"I was very pleased with the goal but in the end their quality counted and we let in four," he added.
Real are on course to meet city rivals Atletico Madrid in the last 16, with Barca the probable opponents in the quarter-finals.
All but two of the last-32, first legs take place at the beginning of December, but Real's has been brought forward because of the European champions' participation in the Club World Cup in mid-December.
Due to the disruption to the La Liga calendar caused by the tournament in Morocco, Sevilla also had their first leg brought forward and they thrashed second-division Sabadell 6-1.
Iago Aspas, who is on loan at the Andalusian club from Liverpool, netted a hat-trick and former Arsenal winger Jose Antonio Reyes scored a long-range stunner as Sevilla all-but assured themselves of a place in the last 16.
The return legs are at the beginning of December, when the Cornella players will fulfill their dream of playing in one of the world's great soccer venues, Real's Bernabeu stadium.
(Writing by Iain Rogers, editing by Toby Davis)
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